Calculus & Numerical Methods
Newton's Law of Cooling
Temperature after time t cooling toward ambient.
Formula
Formula
T = T_a + (T0 − T_a) e−kt
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| T₀ | initial temp | real number (ℝ) | — | input |
| T_a | ambient temp | real number (ℝ) | — | input |
| k | cooling constant | real number (ℝ) | — | input |
| t | time | real number (ℝ) | — | input |
Try it yourself
Interactive calculator
Worked examples
Example 1
GivenT₀ = 90, ambient Tₐ = 20, k = 0.1, time t = 10
Result45.75156088
Example 2
GivenT₀ = 100, ambient Tₐ = 25, k = 0.05, time t = 30
Result41.73476201